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nf_fields • Show schema
{'class_group': [9], 'class_number': 9, 'cm': False, 'coeffs': [1748, -4541, 3914, -171, -646, 171, -38, -38, 0, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 20878097849057792, 'disc_rad': 266, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[3, 3]]], [5, [[3, 1], [2, 3]]], [7, [0]], [11, [[9, 1]]], [13, [[3, 1], [2, 3]]], [17, [[3, 2], [1, 3]]], [19, [0]], [23, [[2, 3], [1, 3]]], [29, [[6, 1], [3, 1]]], [31, [[6, 1], [3, 1]]], [37, [[6, 1], [1, 3]]], [41, [[9, 1]]], [43, [[3, 3]]], [47, [[6, 1], [3, 1]]], [53, [[3, 1], [2, 3]]], [59, [[3, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [243, 108, 144], 'galois_label': '9T20', 'galt': 20, 'grd': 141.7795371895746, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '9.3.20878097849057792.3', 'local_algs': ['2.1.0.1', '2.1.0.1', '2.1.0.1', '2.6.9.5', '7.3.0.1', '7.6.4.2', '19.9.8.2'], 'minimal_sibling': [-322, -350, -189, 335, -35, 29, 37, -15, -3, 1], 'monogenic': -1, 'num_ram': 3, 'r2': 3, 'ramps': [2, 7, 19], 'rd': 65.0577429284, 'regulator': {'__RealLiteral__': 0, 'data': '41799.8473316', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['7.13.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{15716925427}{926091877660} a^{8} - \\frac{292869233}{926091877660} a^{7} - \\frac{689366007539}{926091877660} a^{6} - \\frac{149325263765}{185218375532} a^{5} + \\frac{1620089523773}{231522969415} a^{4} + \\frac{77660736351}{92609187766} a^{3} - \\frac{21901193480167}{926091877660} a^{2} + \\frac{23259935003631}{926091877660} a - \\frac{2025496828184}{231522969415} \\)', '\\( \\frac{13228646}{1474668595} a^{8} + \\frac{8793486}{1474668595} a^{7} - \\frac{502891012}{1474668595} a^{6} - \\frac{165702210}{294933719} a^{5} + \\frac{1901832686}{1474668595} a^{4} - \\frac{1420869510}{294933719} a^{3} - \\frac{7938138136}{1474668595} a^{2} + \\frac{47143951818}{1474668595} a - \\frac{24983432963}{1474668595} \\)', '\\( \\frac{5489698}{3795458515} a^{8} + \\frac{8722858}{3795458515} a^{7} - \\frac{224292316}{3795458515} a^{6} - \\frac{67753289}{759091703} a^{5} + \\frac{246695483}{3795458515} a^{4} - \\frac{874859310}{759091703} a^{3} - \\frac{1441548953}{3795458515} a^{2} + \\frac{7103859419}{3795458515} a - \\frac{4231657689}{3795458515} \\)', '\\( \\frac{1515007111}{231522969415} a^{8} - \\frac{877385904}{231522969415} a^{7} - \\frac{49325712692}{231522969415} a^{6} - \\frac{8311932652}{46304593883} a^{5} + \\frac{30383220871}{231522969415} a^{4} - \\frac{183078257227}{46304593883} a^{3} + \\frac{753547321934}{231522969415} a^{2} + \\frac{128849400643}{231522969415} a + \\frac{2217384832317}{231522969415} \\)', '\\( \\frac{200062853}{463045938830} a^{8} - \\frac{866208907}{463045938830} a^{7} - \\frac{6873565101}{463045938830} a^{6} + \\frac{3411858243}{92609187766} a^{5} + \\frac{4218994544}{231522969415} a^{4} - \\frac{21292836974}{46304593883} a^{3} + \\frac{668159469067}{463045938830} a^{2} - \\frac{799891353811}{463045938830} a + \\frac{169169010963}{231522969415} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/1852183755320*a^8 + 568263161381/1852183755320*a^7 - 198915009677/1852183755320*a^6 + 67961834013/370436751064*a^5 + 82118358567/231522969415*a^4 - 11224639959/185218375532*a^3 - 410248015281/1852183755320*a^2 + 462038110253/1852183755320*a + 156586408423/463045938830']}
Number field data - 9.3.20878097849057792.3